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A note on the Galambos copula and its associated Bernstein function

100%

Mai J.-F.

Dependence Modeling

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2014

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tom 2

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nr 1

EN

There is an infinite exchangeable sequence of random variables {Xk}k∈ℕ such that each finitedimensional distribution follows a min-stable multivariate exponential law with Galambos survival copula, named after [7]. A recent result of [15] implies the existence of a unique Bernstein function Ψ associated with {Xk}k∈ℕ via the relation Ψ(d) = exponential rate of the minimum of d members of {Xk}k∈ℕ. The present note provides the Lévy–Khinchin representation for this Bernstein function and explores some of its properties.

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Geometrically strictly semistable laws as the limit laws

86%

Malinowski M.

Discussiones Mathematicae Probability and Statistics

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2007

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tom 27

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nr 1-2

79-97

EN

A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable $X_p$ such that $X\stackrel{d}{=} ∑_{k=1}^{T(p)}X_{p,k}$, where $X_{p,k}$'s are i.i.d. copies of $X_p$, and random variable T(p) independent of ${X_{p,1},X_{p,2},...}$ has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions. We show that they are limit laws for random and deterministic sums of independent random variables.

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On some limit distributions for geometric random sums

72%

Malinowski M.

Discussiones Mathematicae Probability and Statistics

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2008

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tom 28

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nr 2

247-266

EN

We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward transfered to the case of random vectors in $ℝ^d$.

Ograniczanie wyników

2 Discussiones Mathematicae Probability and Statistics

1 Dependence Modeling

2 Malinowski M.

1 Mai J.-F.

1 2014

1 2008

1 2007

A note on the Galambos copula and its associated Bernstein function

Geometrically strictly semistable laws as the limit laws

On some limit distributions for geometric random sums